Finite Group Databasebeta

← C8×(C2×#261)⋊C4 #16785182

Subgroups — C8×(C2×#261)⋊C4 #16785182

Order 3328.

1174 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×#261C212yesmaximal
2#13130497C211yesmaximal, characteristic
3C2×(C2×#261)⋊C8C212yesmaximal
4C4×(C2×#261)⋊C4C211yesmaximal, characteristic
5C2×C4×C8×D13C211yesmaximal, characteristic
6C22×C4×#261C2212yes—
7C22×D13⋊C8C2212yes—
8C22×C8×D13C2211yescharacteristic
9C22×C8×D13C2211yescharacteristic
10C2×C42×D13C2211yescharacteristic
11C2×(C2×#261)⋊C4C414yes—
12C2×C8×#261—24no—
13C2×C8×#261—24no—
14C2×C8×#261C418yescomplemented
15C2×C4×C8×C13C411yescharacteristic, complemented
16C2×C8×Dic13C411yescharacteristic, complemented
17C2×C8×Dic13C411yescharacteristic, complemented
18C2×C4×#1055C411yescharacteristic, complemented
19C4×C8×D13—24no—
20#11718290C414yescomplemented
21(C2×#261)⋊C8C418yescomplemented
22C23×#261C2×C414yes—
23C22×C4×D13C2×C412yes—
24C22×C4×D13C2311yescharacteristic
25C22×#1057C2×C414yes—
26C2×C4×#261—22no—
27C2×C4×#261—22no—
28C2×C4×#261—22no—
29C2×C4×#261—22no—
30C2×C4×#261C2×C414yes—
31C2×C4×#261C2×C414yes—
32C2×D13⋊C8—22no—
33C2×D13⋊C8—22no—
34C2×D13⋊C8—22no—
35C2×D13⋊C8—22no—
36C2×D13⋊C8C2×C414yes—
37C2×D13⋊C8C2×C414yes—
38C22×C8×C13C2×C411yescharacteristic
39C22×C8×C13C2×C411yescharacteristic
40C2×C42×C13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13C2×C412yes—
43C22×#1055C2×C411yescharacteristic
44C22×#1055C2×C411yescharacteristic
45C2×C8×D13—22no—
46C2×C8×D13—21no—
47C2×C8×D13—21no—
48C2×C8×D13C2×C414yes—
49C2×C8×D13C2×C414yes—
50C2×C8×D13D412yes—
51C2×C8×D13D414yes—
52C2×C8×D13Q812yes—
53C42×D13—22no—
54C42×D13—22no—
55(C2×#261)⋊C4C8116yesdirect product factor
56C8×#261—216no—
57C4×C8×C13—22no—
58C8×Dic13—22no—
59C8×Dic13—22no—
60C4×#1055—22no—
61C8×#95—131nomaximal, Sylow
62C23×D13C22×C411yescharacteristic
63C22×#261—24no—
64C22×#261—24no—
65C22×#261—28no—
66C22×#261C4218yes—
67C22×#261C2×C8116yes—
68C22×C4×C13C4212yes—
69C22×C4×C13C22×C411yescharacteristic
70C22×Dic13C4212yes—
71C22×Dic13C22×C411yescharacteristic
72C2×C4×D13—24no—
73C2×C4×D13—24no—
74C2×C4×D13C2×C818yes—
75C2×C4×D13C22×C412yes—
76C2×C4×D13C22×C412yes—
77C2×C4×D13C2×D411yescharacteristic
78C2×C4×D13C2×D412yes—
79C2×C4×D13C2×Q811yescharacteristic
80C2×C4×D13#4111yescharacteristic
81C2×C4×D13#4111yescharacteristic
82C2×C4×D13#4112yes—
83C2×#1057—24no—
84C2×#1057—24no—
85C2×#1057C4218yes—
86C4×#261—24no—
87C4×#261—24no—
88C4×#261—24no—
89C4×#261—24no—
90D13⋊C8—24no—
91D13⋊C8—24no—
92D13⋊C8—24no—
93D13⋊C8—24no—
94C2×C8×C13—21no—
95C2×C8×C13—21no—
96C2×C8×C13C4212yes—
97C2×C8×C13C4212yes—
98C2×C8×C13C22⋊C412yes—
99C2×C8×C13C4⋊C412yes—
100C42×C13—21no—
101C42×C13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13—24no—
105C2×#1055—21no—
106C2×#1055—21no—
107C2×#1055C4212yes—
108C2×#1055C4212yes—
109C2×#1055C22⋊C412yes—
110C2×#1055C4⋊C412yes—
111C8×D13—24no—
112C8×D13—24no—
113C8×D13C22⋊C418yes—
114C8×D13C4⋊C418yes—
115C22×C4×C8—132no—
116C22×C4×C8—131no—
117C2×#336—131no—
118C2×#336—132no—
119C4×#95—131no—
120C23×C13C2×C4211yescharacteristic
121C22×D13C2×C4212yes—
122C22×D13C4×D411yescharacteristic
123C22×D13C4×D412yes—
124C22×D13C4×Q811yescharacteristic
125C22×D13C22×C814yes—
126C22×D13#13114yes—
127C2×#261—28no—
128C2×#261—28no—
129C2×#261—216no—
130C2×#261—216no—
131C2×#261C4×C8116yescomplemented
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13C4×C814yescomplemented
135C2×C4×C13C2×C4211yescharacteristic
136C2×C4×C13C2×C4211yescharacteristic
137C2×C4×C13C2×C22⋊C411yescharacteristic
138C2×C4×C13C2×C4⋊C411yescharacteristic
139C2×C4×C13#11711yescharacteristic
140C2×C4×C13#11711yescharacteristic
141C2×Dic13—22no—
142C2×Dic13—22no—
143C2×Dic13C4×C814yescomplemented
144C2×Dic13C2×C4212yes—
145C2×Dic13C4×D411yescharacteristic
146C2×Dic13C4×D412yes—
147C2×Dic13C4×Q811yescharacteristic
148C4×D13—216no—
149C4×D13C2×C22⋊C412yes—
150C4×D13C2×C4⋊C412yes—
151C4×D13#11712yes—
152C4×D13#11712yes—
153C4×D13C4×D412yes—
154C4×D13C4×D412yes—
155C4×D13C4×D412yes—
156C4×D13C4×Q812yes—
157#1057—28no—
158C8×C13—22no—
159C8×C13#9514yescomplemented
160#1055—22no—
161#1055#9514yescomplemented
162C23×C8—131no—
163C23×C8—132no—
164C23×C8—131no—
165C22×C42—132no—
166C22×C42—131no—
167C2×C4×C8—138no—
168C2×C4×C8—131no—
169C2×C4×C8—131no—
170C2×C4×C8—131no—
171C2×C4×C8—264no—
172C2×C4×C8—264no—
173C2×C4×C8—264no—
174C2×C4×C8#26111yescharacteristic, complemented
175C2×#95—134no—
176#336—138no—
177#336—134no—
178C22×C13C4311yescharacteristic
179C22×C13C4×C22⋊C411yescharacteristic
180C22×C13C4×C4⋊C411yescharacteristic
181C22×C13C2×C4×C812yes—
182C22×C13#40512yes—
183C2×D13C4×C22⋊C412yes—
184C2×D13C4×C4⋊C412yes—
185C2×D13C2×C4×C814yes—
186C2×D13#40514yes—
187C2×D13C8×D414yes—
188C2×D13C8×D418yes—
189C2×D13C8×Q814yes—
190#261—216no—
191C4×C13—24no—
192C4×C13C2×#9511yescharacteristic
193C4×C13#37611yescharacteristic
194C4×C13C4×C22⋊C411yescharacteristic
195C4×C13C4×C4⋊C411yescharacteristic
196Dic13—24no—
197Dic13C4×C22⋊C412yes—
198Dic13C4×C4⋊C412yes—
199C23×C4—131no—
200C23×C4—134no—
201C23×C4—132no—
202C22×C8—131no—
203C22×C8—134no—
204C22×C8—132no—
205C22×C8—132no—
206C22×C8—134no—
207C22×C8—134no—
208C22×C8—134no—
209C22×C8—134no—
210C22×C8—131no—
211C22×C8—134no—
212C22×C8—261no—
213C22×C8—261no—
214C22×C8—262no—
215C22×C8—262no—
216C22×C8—262no—
217C22×C8—262no—
218C22×C8—262no—
219C22×C8C2×#26111yescharacteristic
220C22×C8C2×#26111yescharacteristic
221C2×C42—134no—
222C2×C42—134no—
223C2×C42—132no—
224C2×C42—131no—
225C2×C42—262no—
226C2×C42—262no—
227C2×C42—262no—
228C2×C42—262no—
229C2×C42—262no—
230C2×C42—262no—
231C2×C42C2×#26111yescharacteristic
232C4×C8—22no—
233C4×C8—262no—
234C4×C8—262no—
235C4×C8—2616no—
236C4×C8—262no—
237#95—1316no—
238C2×C13C4×#9511yescharacteristic
239C2×C13C42×C811yescharacteristic
240C2×C13#172611yescharacteristic
241C2×C13C8×C22⋊C412yes—
242C2×C13C8×C4⋊C412yes—
243D13C8×C22⋊C414yes—
244D13C8×C4⋊C414yes—
245C24—131no—
246C22×C4—131no—
247C22×C4—132no—
248C22×C4—132no—
249C22×C4—131no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—132no—
253C22×C4—131no—
254C22×C4—132no—
255C22×C4—1316no—
256C22×C4—138no—
257C22×C4—132no—
258C22×C4—138no—
259C22×C4—264no—
260C22×C4—264no—
261C22×C4—264no—
262C22×C4—264no—
263C22×C4—268no—
264C22×C4C4×#26112yes—
265C22×C4C22×#26111yescharacteristic
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—132no—
269C2×C8—132no—
270C2×C8—132no—
271C2×C8—138no—
272C2×C8—138no—
273C2×C8—138no—
274C2×C8—132no—
275C2×C8—264no—
276C2×C8—264no—
277C2×C8—264no—
278C2×C8—264no—
279C2×C8—264no—
280C2×C8—264no—
281C2×C8—264no—
282C2×C8—264no—
283C2×C8—261no—
284C2×C8—261no—
285C2×C8C4×#26112yes—
286C2×C8C4×#26112yes—
287C2×C8C4⋊#26112yes—
288C2×C8C22⋊#26112yes—
289C42—21no—
290C42—21no—
291C42—264no—
292C42—264no—
293C42—264no—
294C42—264no—
295C42—264no—
296C42—261no—
297C42—261no—
298C13C8×#9511yescharacteristic, complemented, Sylow
299C23—132no—
300C23—131no—
301C23—131no—
302C23—134no—
303C23—134no—
304C23—132no—
305C23C2×C4×#26111yescharacteristic
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—132no—
309C2×C4—131no—
310C2×C4—131no—
311C2×C4—132no—
312C2×C4—132no—
313C2×C4—132no—
314C2×C4—132no—
315C2×C4—132no—
316C2×C4—132no—
317C2×C4—132no—
318C2×C4—132no—
319C2×C4—132no—
320C2×C4—1316no—
321C2×C4—134no—
322C2×C4—2616no—
323C2×C4—268no—
324C2×C4—2616no—
325C2×C4—2616no—
326C2×C4—268no—
327C2×C4—262no—
328C2×C4—262no—
329C2×C4C8×#26114yescomplemented
330C2×C4C2×C4×#26111yescharacteristic
331C2×C4C2×C4×#26111yescharacteristic
332C2×C4C2×C4⋊#26111yescharacteristic
333C2×C4#8823711yescharacteristic
334C2×C4#8823711yescharacteristic
335C2×C4C2×C22⋊#26111yescharacteristic
336C8—22no—
337C8—134no—
338C8—268no—
339C8—262no—
340C8(C2×#261)⋊C414yesdirect product factor
341C22—132no—
342C22—132no—
343C22—138no—
344C22—134no—
345C22—134no—
346C22—134no—
347C22—134no—
348C22C42×#26111yescharacteristic
349C22C4×C4⋊#26111yescharacteristic
350C22C2×C8×#26112yes—
351C22#1171908912yes—
352C22C4×C22⋊#26111yescharacteristic
353C4—24no—
354C4—132no—
355C4—132no—
356C4—2616no—
357C4—264no—
358C4#1171905711yescharacteristic
359C4C4×C4⋊#26111yescharacteristic
360C4C2×(C2×#261)⋊C411yescharacteristic
361C4C4×C22⋊#26111yescharacteristic
362C2—134no—
363C2—134no—
364C2C4×(C2×#261)⋊C411yescharacteristic
365C2C4×C8×#26111yescharacteristic
366C2#1313049211yescharacteristic
367C2C8×C22⋊#26112yes—
368C2C8×C4⋊#26112yes—
subgroupG/H
centerC22×C8C2×#261
commutatorC2×C13C42×C8
FrattiniC22×C4C22×#261
FittingC2×C4×C8×C13C4
socleC23×C13C2×C42
prime radicalC23×D13C22×C4
cosocleC22×C4×D13C23
hypercenterC2×C4×C8#261
hypocenterC13C8×#95
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
14. C2×C8×#261C4semidirect
15. C2×C4×C8×C13C4semidirect
16. C2×C8×Dic13C4semidirect
17. C2×C8×Dic13C4semidirect
18. C2×C4×#1055C4semidirect
20. #11718290C4semidirect
21. (C2×#261)⋊C8C4semidirect
55. (C2×#261)⋊C4C8direct (N × H)
131. C2×#261C4×C8semidirect
134. C2×C4×C13C4×C8semidirect
143. C2×Dic13C4×C8semidirect
159. C8×C13#95semidirect
161. #1055#95semidirect
174. C2×C4×C8#261semidirect
298. C13C8×#95semidirect
329. C2×C4C8×#261semidirect
340. C8(C2×#261)⋊C4direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C8×#2612
#131304972
C2×(C2×#261)⋊C82
C4×(C2×#261)⋊C42
C2×C4×C8×D132
C8×#9513